Broad-band low-inductance cables for making Kelvin connections to electrochemical cells and batteries

ABSTRACT

A broad-band technique for reducing the distributed inductance of a four-conductor Kelvin cable is disclosed. A special inductance-canceling cable section is connected in tandem with the cable section contacting the cell/battery. Connections between the two cable sections are transposed such that conductors in each conductor pair of the canceling section connect to current-carrying and voltage-sensing conductors from different conductor pairs in the contacting section. The canceling section thereby exhibits a distributed negative mutual inductance between its current-carrying and voltage-sensing conductors that can effectively cancel the distributed positive mutual inductance introduced by the contacting section. 
     In one embodiment, conductor pairs comprise pairs of insulated wires which may be twisted together. In other disclosed embodiments, conductor pairs comprise shielded coaxial cables.

BACKGROUND OF THE INVENTION

The present invention relates to measuring a dynamic parameter (e.g.,impedance, admittance, resistance, reactance, conductance, susceptance)of an electrochemical cell or battery. More specifically, it relates toreducing the effects of cable inductance upon electrical measurementsimplemented with time-varying signals through Kelvin (i.e., four-point)connections.

Measuring automotive and standby cell/battery parameters withtime-varying signals (i.e., measuring dynamic parameters) are nowcommonly accepted maintenance and diagnostic procedures. (See, e.g.,U.S. Pat. Nos. 5,140,269, 6,262,563, 6,534,993, and 6,623,314). Becauseof the very small impedances of such cells/batteries, Kelvin connectionsare routinely employed to reduce the influence of contact andinterconnecting cable impedance. Kelvin connections make contact witheach cell/battery terminal at two separate contact points—one forcurrent and one for voltage. Apparatus for measuring a two-terminalcell/battery by means of Kelvin connections therefore requires afour-wire interconnecting cable.

Kelvin connections very effectively remove the spurious effects of cableand contact resistances when measurements are made with static currentsand voltages. However, when measuring with time-varying signals,distributed mutual inductance between current-carrying andvoltage-sensing conductors in the interconnecting cable can introducesignificant errors.

Consider FIG. 1. FIG. 1 depicts cell/battery 10 connected to measuringapparatus 20 by means of four-wire cable 30, Y-junction 40, and Kelvinconductors A, B, C, and D. Current-carrying conductors A and B couple topositive and negative cell/battery terminals at contact points 50 and60, respectively. Voltage-sensing conductors C and D separately coupleto positive and negative cell/battery terminals at contact points 70 and80, respectively. During dynamic measurements, a time-varying currentflows through current-carrying conductors A and B and also flowsinternally between the terminals along an internal current path 90.

FIG. 2 shows the arrangement of conductors employed in the apparatus ofFIG. 1. This arrangement was first introduced by Champlin in U.S. Pat.No. 3,873,911 and has been commonly used in dynamic testing of lead-acidstorage batteries since 1975. FIG. 2 discloses contacting cable section5 comprising an A-C pair of insulated wires 120 coupling to the positivecell/battery terminal and a B-D pair of insulated wires 130 coupling tothe negative cell/battery terminal. The two conductor pairs arenecessarily spaced-apart at the cell/battery terminals but are broughtinto close proximity at Y-junction 40. These insulated wire pairs may,or may not, be twisted together in section 5. At Y-junction 40 the fourwires are re-arranged for connection to zero-coupling cable section 15.Throughout section 15, the A-B current carrying conductors and the C-Dvoltage-sensing conductors are separately paired and twisted together,pair 140 and pair 150, respectively. The advantage of this pairing andtwisting arrangement is that transverse magnetic fields—inherentlypresent in space 35 of cable section 5—are virtually non-existent inspace 75 of cable section 15 by virtue of the twisted current-carryingconductors A and B. In addition, the twisted voltage-sensing conductorsC and D exhibit negligible coupling to whatever small magnetic fields doexist in space 75. Accordingly, over-all cable inductance is largelyconfined to contacting cable section 5 with virtually no contributionfrom zero-coupling cable section 15. Zero-coupling section 15 cantherefore be of any length desired for convenience.

Because of the necessity for physically-separated current-carryingconductors and for physically-separated voltage-sensing conductors incable section 5, inductance is unavoidable in that section. Let ω=2πf bethe angular measurement frequency, j=√{square root over (−1)}, and letRe( ) stand for “the real part of”. For a time-varying currenti_(AB)(t)=Re(Î_(AB)·e^(jωt)) flowing in conductors A and B, atime-varying transverse magnetic field H(t)=Re({circumflex over(H)}·e^(jωt)) is generated in space 35 between the two current-carryingconductors of section 5. Ampere's Law states that phasor (complex)quantities {circumflex over (H)} and Î_(AB) are related by

{circumflex over (H)}·dl=Î _(AB)  (1)where the integral extends over any closed contour surrounding acurrent-carrying conductor. For an ac current entering cell/battery 10on conductor A and leaving on conductor B, the direction of the(complex) magnetic field vector {circumflex over (H)} is as shown inFIG. 1. The transverse magnetic field therefore emerges from the planeof the conductors in space 35 of cable section 5 as is shown in FIG. 2.

Voltage-sensing conductors C and D in cable section 5 along withconducting path 90 through cell/battery 10 form a closed loop. Accordingto Faraday's law of induction, any time-varying magnetic field linkingthis loop will induce a time-varying voltage into the voltage-sensingcircuit. For a complex magnetic field vector {circumflex over (H)}, thecomplex ac voltage {circumflex over (V)}_(CD) induced into thevoltage-sensing circuit is{circumflex over (V)} _(CD) =jωμ ₀

{circumflex over (H)}·dS   (2)where μ₀ is the magnetic permeability of free space, and dS is adifferential area vector perpendicular to a surface bounded by theclosed loop.

Thus, with time-varying signals, the time-varying magnetic field formedin space 35 of cable section 5 introduces distributed coupling betweenthe current-carrying circuit and the voltage-sensing circuit. Suchspurious coupling is fundamental to the geometry of FIGS. 1 and 2 andtends to defeat the effectiveness of the Kelvin connections.

One can define the mutual inductance between the current-carrying A-Bcircuit and the voltage-sensing C-D circuit as follows:

$\begin{matrix}{M_{{AB},{CD}} = {\frac{{\overset{\Cap}{V}}_{CD}}{{j\omega}\;{\overset{\Cap}{I}}_{AB}} = \frac{\mu_{0}{∯{\hat{\underset{\_}{H}} \cdot \underset{\_}{\mathbb{d}S}}}}{{\overset{\Cap}{I}}_{AB}}}} & (3)\end{matrix}$

Mutual inductance M_(AB,CD) is a distributed parameter—distributed overthe entire length of contacting cable section 5. In any dynamicmeasurement, a magnetically-induced voltage{circumflex over (V)} _(CD) =jωM _(AB,CD) ·Î _(AB)  (4)will be developed in the voltage-sensing circuit along with the normalac voltage developed across cell/battery 10. Accordingly, as shown inFIG. 3, the complete cell/battery impedance measured with Kelvinconnections appears externally to beZ _(MEAS) =Z _(BAT) +jωM _(AB,CD)  (5)

Distributed mutual inductance M_(AB,CD) is a positive quantity thatappears in series with cell/battery impedance Z_(BAT). It iselectrically indistinguishable from a lumped self-inductance L_(BAT)internal to the battery. For sufficiently small Z_(BAT) or sufficientlylarge ω, the part of Equation (5) associated with the Kelvin cables maydominate. This fact constitutes the fundamental problem with dynamicmeasurements performed through Kelvin connections.

PRIOR ART

A method for reducing the influence of inductance of Kelvin cables hasbeen taught by Bertness in U.S. Pat. No. 6,172,505. This method isdepicted in FIG. 4. Y-junction 40 in FIG. 4 contains transformer 90having primary winding 95 placed in series with current-carrying Kelvinconductor A and secondary winding 100 placed in series withvoltage-sensing Kelvin conductor C. Windings 95 and 100 are wound inopposite directions on an iron core 110 so that the voltage induced intocoil 100 by current flowing in coil 95 opposes the voltage normallyinduced into the voltage-sensing C-D circuit by current flowing in thecurrent-carrying A-B circuit. Accordingly, transformer 90 introduces alumped negative mutual inductance that can be adjusted to cancel thedistributed positive mutual inductance inherently present in cablesection 5.

Although the inductance cancellation method of FIG. 4 can be quiteeffective, there are several problems with its use. First of all, for agiven magnetic core, the only way to change the transformer's mutualinductance is to vary the number of turns on its windings. That makesthe transformer's mutual inductance a difficult quantity to adjust.Secondly, the core's hysteresis and eddy current losses introduceresistive terms into the transformer's equivalent circuit that can causesignificant measurement errors. Third, the magnetic permeability of aferromagnetic core, and hence the transformer's mutual inductance, isfrequency dependent. As a result, effective cancellation of cableinductance may only occur over a fairly narrow range of frequencies.These and other problems are solved by the invention embodimentsdisclosed below.

SUMMARY OF THE INVENTION

A broad-band technique for canceling the distributed inductance of afour-conductor Kelvin contacting cable section comprising twospaced-apart conductor pairs with each conductor pair comprising acurrent-carrying conductor and a voltage-sensing conductor. A specialcanceling cable section, also comprising spaced-apart conductor pairs,is connected in tandem with the contacting cable section. Connectionsbetween the two cable sections are transposed such that conductors ineach conductor pair of the canceling section connect to current-carryingand voltage-sensing conductors from different conductor pairs in thecontacting section. The canceling section thereby exhibits a distributednegative mutual inductance that can effectively cancel the distributedpositive mutual inductance of the contacting section.

In one embodiment, conductor pairs comprise pairs of insulated wireswhich may be twisted together. In several other disclosed embodiments,conductor pairs comprise shielded coaxial cables.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing illustrating dynamic parameter measuring apparatusconnected to a cell/battery by means of Kelvin (four-point) connections.

FIG. 2 is a schematic representation showing the conductor arrangementmost commonly employed with the apparatus of FIG. 1.

FIG. 3 is an equivalent circuit showing total ac impedance measuredusing the apparatus of FIGS. 1 and 2.

FIG. 4 is a schematic diagram depicting the method for canceling Kelvincable inductance taught by Bertness in U.S. Pat. No. 6,172,505.

FIG. 5 is a schematic diagram depicting a method for implementinginductance cancellation in a Kelvin cable according to one embodiment ofthe present invention.

FIG. 6 is a schematic diagram depicting a method for implementinginductance cancellation in a Kelvin cable according to anotherembodiment of the present invention.

FIG. 7 is a schematic diagram depicting a method for implementinginductance cancellation in a Kelvin cable according to still anotherembodiment of the present invention.

FIG. 8 is a plan drawing showing the dimensions of shielded coaxialconductors comprising the conductor pairs in cable section 5 of theKelvin cables depicted in FIGS. 6 and 7.

FIG. 9 is a calculated plot of distributed mutual inductance M₁ as afunction of conductor separation W₁ at the cell/battery terminals forthe shielded coaxial conductors of the cable section 5 illustrated inFIG. 8.

FIG. 10 is a plan drawing showing the dimensions of parallel shieldedcoaxial conductors comprising the conductor pairs in cable section 25 ofthe Kelvin cables depicted in FIGS. 6 and 7.

FIG. 11 is a calculated plot of normalized distributed mutual inductance(M₂/L₂) as a function of normalized conductor separation (W₂/d_(o)) forthe parallel shielded coaxial conductors of the cable section 25illustrated in FIG. 10.

DETAILED DESCRIPTION OF THE ILLUSTRATIVE EMBODIMENTS

Consider the invention embodiment disclosed in FIG. 5. This figuredepicts Kelvin connections made to battery 10 by means of a conductorarrangement similar to that of FIG. 2, but with an importantmodification. In FIG. 5, an additional cable section, canceling cablesection 25, has been inserted in tandem between cable sections 5 and 15.Canceling cable section 25 comprises two spaced-apart conductor pairs,160 and 170, each comprising two insulated wires which may, or may not,be twisted together. By virtue of transposed connections made inY-junction 40 and in cable junction 55, the roles of conductor pairs insections 5 and 15 are exactly the same as those in sections 5 and 15 ofFIG. 2. Conductor pairs in section 25, however, comprise acurrent-carrying conductor B paired with a voltage-sensing conductor C(pair 160), and a current-carrying conductor A paired with avoltage-sensing conductor D (pair 170).

Because current-carrying conductors A and B in section 25 are transposedfrom those of current-carrying conductors of section 5, the direction ofthe magnetic field in space 45 is opposite to that of the magnetic fieldin space 35. Voltage-sensing conductors are, however, positioned thesame in both sections. Thus, voltages induced into the voltage-sensingcircuit by currents in the current-carrying circuit have opposite signsin the two sections. Section 25 therefore exhibits a negative mutualinductance that can be utilized to cancel the positive mutual inductanceinherent to section 5. However, in contrast with the lumped negativemutual inductance introduced by the transformer in the prior art methodof FIG. 4, the mutual inductance of section 25 is a distributedquantity.

This same distributed negative mutual inductance would occur ifconnections to the voltage-sensing conductors, rather than to thecurrent-carrying conductors, were transposed in going from section 5 tosection 25. A distributed negative mutual inductance in section 25requires only that connections to two of the conductors be transposedbetween sections 5 and 25 such that a voltage-sensing conductor from oneconductor pair of section 5 is paired with a current-carrying conductorfrom the other conductor pair of section 5, and vice-versa.

The distributed negative mutual inductance introduced by this method isa very broad-band property that is essentially loss-free over a widerange of frequencies. These are very desirable advantages over theprior-art method of producing lumped negative mutual inductance depictedin FIG. 4. The distributed negative mutual inductance of the FIG. 5embodiment can be varied by changing either the length of cable section25 or the spacing between conductor pairs 160 and 170. Therefore, themutual inductance of a Kelvin cable of the type depicted in FIG. 5 isfairly easy to “tune” experimentally. One disadvantage of the embodimentdepicted in FIG. 5, however, is that its insulated-wire geometry is notvery amenable to exact mathematical analysis.

FIGS. 6 and 7 disclose invention embodiments that are amenable to exactmathematical analyses and therefore do not require experimental“tuning”. With both of these embodiments, the insulated-wire conductorpairs of cable sections 5 and 25 of FIG. 5 have been replaced byshielded coaxial cables.

In cable section 5 of FIGS. 6 and 7, a coaxial cable 180 replacesconductor pair 120 and couples to the positive terminal of cell/battery10 at contact points 50 and 70, while a coaxial cable 190 replacesconductor pair 130 and couples to the negative terminal of cell/battery10 at contact points 60 and 80. With the coaxial cables depicted, cableshields comprise the current-carrying conductors, A and B, and centerconductors comprise the voltage-sensing conductors, C and D. However,the reciprocity theorem reveals that the distributed mutual inductanceof section 5 will be unchanged by interchanging the roles of coaxialcable shields and center conductors. Therefore, the selection shown inFIGS. 6 and 7 is simply a matter of choice.

In cable section 25 of FIGS. 6 and 7, coaxial cable 200 replacesconductor pair 160 and coaxial cable 210 replaces conductor pair 170.Again, with the coaxial cables depicted, cable shields comprisecurrent-carrying conductors A and B and center conductors comprisevoltage-sensing conductors C and D. Again this selection is simply amatter of choice since the reciprocity theorem likewise reveals that thedistributed mutual inductance of section 25 is unaffected byinterchanging roles of the coaxial shields and center conductors.

In the embodiment of FIG. 7, the conductor pairs in zero-coupling cablesection 15 have also been replaced by shielded coaxial cables. However,in the FIG. 6 embodiment, they remain twisted pairs as in the embodimentof FIG. 5. Either of these choices provides negligible coupling betweencurrent-carrying conductors and voltage-sensing conductors in cablesection 15. Therefore, the selection of one of these two embodimentsover the other is simply a matter of choice.

FIG. 8 is a plan drawing defining dimensions of the shielded coaxialcables that comprise conductors in contacting cable section 5 of theinvention embodiments depicted in FIGS. 6 and 7. One sees that section 5comprises two coplanar coaxial cables having radii d_(i) of their innerconductors, radii d_(o) of their outer conductors, lengths L₁, andseparated at the cell/battery terminals by a distance W₁. Thedistributed mutual inductance of this geometry can be determined exactlyfrom Maxwell's equations. The result is

$\begin{matrix}{M_{1} = {\left( \frac{\mu_{0} \cdot L_{1}}{\pi} \right) \cdot \left\{ {{\left( {1 + \frac{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{0}}{4 \cdot L_{1}} \right)}{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}} \right) \cdot {\ln\left( {1 + \frac{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{0}}{4 \cdot L_{1}} \right)}} \right)}} - 1} \right\}}} & (6)\end{matrix}$Note that M ₁ is unaffected by the coax cables' center-conductordiameter d_(i).

FIG. 9 shows a plot of distributed mutual inductance M₁ calculated fromEquation (6) by assuming that section 5 comprises two 12-inch (30.48 cm)lengths of conventional RG-6/U coaxial cable (d_(o)=0.25″) (6.35 mm).One notes that M₁ varies quite gradually with W₁ over most of the rangeof W₁. However, as W₁ approaches its maximum value of 24 inches (60.96cm), mutual inductance M₁ drops precipitously to zero.

FIG. 10 is a plan drawing defining the dimensions of the shieldedcoaxial conductors comprising conductors in canceling cable section 25of the Kelvin cables depicted in FIGS. 6 and 7. One observes twoparallel coaxial cables having radii d_(i) of their inner conductors,radii d_(o) of their outer conductors, lengths L₂, and uniformlyseparated by distance W₂. The distributed mutual inductance of thisgeometry can likewise be determined exactly from Maxwell's equations.The result is

$\begin{matrix}{M_{2} = {\left( \frac{{- \mu_{0}} \cdot L_{2}}{\pi} \right) \cdot {\ln\left( {1 + \frac{2 \cdot W_{2}}{d_{0}}} \right)}}} & (7)\end{matrix}$Note that M₂ is likewise unaffected by the coax cables' center-conductordiameter d_(i).

FIG. 11 is a plot of normalized distributed mutual inductance (M₂/L₂) asa function of normalized conductor separation (W₂/d_(o)) calculated fromEquation (7). One sees that (M₂/L₂) decreases logarithmically as(W₂/d_(o)) increases linearly throughout most of the range plotted.

One can utilize equations (6) and (7) to design broadband low-inductanceKelvin cables of the type disclosed in FIGS. 6 and 7. As a designexample, consider test leads in section 5 comprising a pair of two 12″(30.48 cm) lengths of RG-6/U coaxial cable. Equation (6) predicts thatthe distributed mutual inductance of this section will be M₁=0.39±0.05μH over the range 5″≦W₁≦23.5″. According to equation (7), one canrealize a negative mutual inductance M₂=−0.39 μH with a section 25length L₂=17.46″ (44.35 cm) of parallel RG-6/U cables separated bydistance W₂=1″ (2.54 cm). Thus, the tandem combination of these twosections would result in a broadband low-inductance Kelvin cable havingtotal mutual inductance |M₁+M₂|≦0.05 μH over the entire range5″≦W₁23.5″. This value represents a minimum decrease in mutualinductance of nearly an order of magnitude.

The invention embodiments illustrated in FIGS. 5, 6, and 7 all depict acanceling cable section 25, inserted between a contacting cable section5, and a zero-coupling cable section 15. It should be made clear,however, that the order of this tandem arrangement is somewhatarbitrary. The canceling cable section 25 could just as well be placedafter the zero-coupling cable section in the cascade rather than beforeit. Furthermore, zero-coupling section 15 is only employed to make thetotal cable length convenient. In many cases, a zero-coupling section 15may not be necessary at all.

Moreover, the invention is not limited to the particular geometries andexamples disclosed herein. For instance, pairs of shielded coaxialcables and of twisted insulated wires have both been disclosed inillustrative examples of canceling cable sections. However, otherpassive transmission-line geometries such as elliptical lines, open-wirelines, strip-lines, microstrip lines, etc, can just as well be employed.Furthermore, distributed negative mutual inductance can also be obtainedfrom a spatial distribution of either passive or active elements. Othermeans for implementing a distributed negative mutual inductance sectionwill be apparent to those skilled in the art, and our invention includesany such section obtained by any means whatsoever inserted in tandemwith a Kelvin connecting cable. Workers skilled in the art willrecognize that these and other variations may be made in form and detailwithout departing from the true spirit and scope of our invention.

1. A low-inductance cable for implementing Kelvin connections topositive and negative terminals of an electrochemical cell or batterycomprising: a first cable section adapted to couple to a positiveterminal with a first current-carrying conductor and a first voltagesensing conductor and to couple to a negative terminal with a secondcurrent-carrying conductor and a second voltage-sensing conductor, saidsecond current-carrying and voltage-sensing conductors spaced apart fromsaid first current-carrying and voltage-sensing conductors, a secondcable section comprising a third current-carrying conductor, a thirdvoltage-sensing conductor, a fourth current-carrying conductor, and afourth voltage-sensing conductor, said fourth current-carrying andvoltage sensing conductors spaced apart from said third current-carryingand voltage-sensing conductors; and, a cable junction interposed betweensaid first cable section and said second cable section, said cablejunction transposing connections by interconnecting said first andfourth current-carrying conductors, said second and thirdcurrent-carrying conductors, said first and third voltage-sensingconductors, and said second and fourth voltage-sensing conductors. 2.The low-inductance cable of claim 1 wherein said first current-carryingand voltage-sensing conductors, said second current-carrying andvoltage-sensing conductors, said third current-carrying andvoltage-sensing conductors, and said fourth current-carrying andvoltage-sensing conductors comprise four pairs of insulated wires. 3.The low-inductance cable of claim 2 wherein wires of each said pair aretwisted together.
 4. The low-inductance cable of claim 1 wherein saidfirst current-carrying and voltage-sensing conductors, said secondcurrent-carrying and voltage-sensing conductors, said thirdcurrent-carrying and voltage-sensing conductors, and said fourthcurrent-carrying and voltage-sensing conductors comprise four shieldedcoaxial cables.
 5. The low-inductance cable of claim 4 whereincurrent-carrying and voltage-sensing conductors of said first cablesection couple through a distributed mutual inductance given by equation(6)$M_{1} = {\left( \frac{\mu_{0} \cdot L_{1}}{\pi} \right) \cdot \left\{ {{\left( {1 + \frac{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{o}}{4 \cdot L_{1}} \right)}{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}} \right) \cdot {\ln\left( {1 + \frac{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{o}}{4 \cdot L_{1}} \right)}} \right)}} - 1} \right\}}$and current-carrying and voltage-sensing conductors of said second cablesection couple through a distributed mutual inductance given by equation(7)$M_{2} = {\left( \frac{{- \mu_{0}} \cdot L_{2}}{\pi} \right) \cdot {{\ln\left( {1 + \frac{2 \cdot W_{2}}{d_{o}}} \right)}.}}$6. A connecting cable for providing Kelvin connections to a positiveterminal and a negative terminal of an electrochemical cell or batterycomprising: a first cable section adapted to couple to said positiveterminal with first and second conductors and to couple to said negativeterminal with third and fourth conductors, said third and fourthconductors spaced apart from said first and second conductors, a secondcable section comprising fifth, sixth, seventh, and eighth conductors,said seventh and eighth conductors spaced apart from said fifth andsixth conductors, a third cable section comprising ninth, tenth,eleventh, and twelfth conductors, said eleventh and twelfth conductorsspaced apart from said ninth and tenth conductors, a first cablejunction interposed between said first cable section and said secondcable section, said first cable junction transposing connections byinterconnecting said first and eighth conductors, said second and sixthconductors, said third and seventh conductors, and said fourth and fifthconductors; and a second cable junction interposed between said secondcable section and, said third cable section, said second cable junctiontransposing connections by interconnecting said fifth and tenthconductors, said sixth and eleventh conductors, said seventh and twelfthconductors, and said eighth and ninth conductors.
 7. The connectingcable of claim 6 wherein said first and second conductors, said thirdand fourth conductors, said fifth and sixth conductors, and said seventhand eighth conductors comprise four pairs of insulated wires.
 8. Theconnecting cable of claim 7 wherein insulated wires of each said pairare twisted together.
 9. The connecting cable of claim 6 wherein saidfirst and second conductors, said third and fourth conductors, saidfifth and sixth conductors, and said seventh and eighth conductorscomprise conductors of four shielded coaxial cables.
 10. The connectingcable of claim 6 wherein said ninth and tenth conductors and saideleventh and twelfth conductors comprise two pairs of twisted insulatedwires.
 11. The connecting cable of claim 6 wherein said ninth and tenthconductors and said eleventh and twelfth conductors comprise conductorsof two shielded coaxial cables.
 12. The connecting cable of claim 9wherein coaxial cable shields couple to coaxial cable center conductorsthrough distributed mutual inductances given by equation (6)$M_{1} = {\left( \frac{\mu_{0} \cdot L_{1}}{\pi} \right) \cdot \left\{ {{\left( {1 + \frac{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{o}}{4 \cdot L_{1}} \right)}{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}} \right) \cdot {\ln\left( {1 + \frac{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{o}}{4 \cdot L_{1}} \right)}} \right)}} - 1} \right\}}$in cable section 1 and by equation (7)$M_{2} = {\left( \frac{{- \mu_{0}} \cdot L_{2}}{\pi} \right) \cdot {{\ln\left( {1 + \frac{2 \cdot W_{2}}{d_{o}}} \right)}.}}$in cable section
 2. 13. The connecting cable of claim 11 wherein coaxialcable shields couple to coaxial cable center conductors throughdistributed mutual inductance given by equation (7)$M_{2} = {\left( \frac{{- \mu_{0}} \cdot L_{2}}{\pi} \right) \cdot {{\ln\left( {1 + \frac{2 \cdot W_{2}}{d_{o}}} \right)}.}}$14. A cable for implementing Kelvin connections to first and secondterminals of an electrochemical cell or battery comprising: a firstcable section adapted to couple to said first terminal with a conductorpair comprising a current-carrying conductor and a voltage-sensingconductor and to couple to said second terminal with another conductorpair comprising a current-carrying conductor and a voltage-sensingconductor, a second cable section comprising two spaced-apart conductorpairs, each said pair comprising a current-carrying conductor and avoltage-sensing conductor; and, a cable junction interconnectingconductors of said first and second cable sections, said cable junctiontransposing connections such that conductors in each pair in said firstcable section couple to conductors in different pairs in said secondcable section.
 15. The cable of claim 14 wherein said conductor pairs insaid first and second cable sections comprise pairs of insulated wires.16. The cable of claim 15 wherein insulated wires of each said pair aretwisted together.
 17. The cable of claim 14 wherein said conductor pairsin said first and second cable sections comprise shielded coaxialcables.
 18. The cable of claim 17 wherein current-carrying conductorscouple to voltage-sensing conductors in said first cable section throughdistributed mutual inductance given by equation (6)$M_{1} = {\left( \frac{\mu_{0} \cdot L_{1}}{\pi} \right) \cdot \left\{ {{\left( {1 + \frac{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{o}}{4 \cdot L_{1}} \right)}{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}} \right) \cdot {\ln\left( {1 + \frac{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{o}}{4 \cdot L_{1}} \right)}} \right)}} - 1} \right\}}$and current-carrying conductors couple to voltage-sensing conductors insaid second cable section through distributed mutual inductance given byequation (7)$M_{2} = {\left( \frac{{- \mu_{0}} \cdot L_{2}}{\pi} \right) \cdot {{\ln\left( {1 + \frac{2 \cdot W_{2}}{d_{o}}} \right)}.}}$19. A low-inductance cable for implementing Kelvin connections to firstand second terminals of an electrochemical cell or battery comprising: afirst cable section adapted to couple to said first terminal with onepair of conductors and to couple to said second terminal with anotherpair of conductors, a second cable section comprising two spaced-apartpairs of conductors, a third cable section comprising two spaced-apartpairs of conductors, a first cable junction interconnecting conductorsof said first and second cable sections, said first cable junctiontransposing connections such that conductors in each pair in said firstcable section couple to conductors in different pairs in said secondcable section; and, a second cable junction interconnecting conductorsof said second and third cable sections, said second cable junctiontransposing connections such that conductors in each pair in said secondcable section couple to conductors in different pairs in said thirdcable section.
 20. The low-inductance cable of claim 19 wherein saidpairs of conductors in said first and second cable sections comprisepairs of insulated wires.
 21. The low-inductance cable of claim 20wherein wires in each said pair are twisted together.
 22. Thelow-inductance cable of claim 19 wherein said pairs of conductors insaid first and second cable sections comprise shielded coaxial cables.23. The low-inductance cable of claim 19 wherein said pairs ofconductors in said third cable section comprise pairs of insulated wirestwisted together.
 24. The low-inductance cable of claim 19 wherein saidpairs of conductors in said third cable section comprise shieldedcoaxial cables.
 25. The low-inductance cable of claim 22 wherein mutualinductance coupling between coaxial cable shields and center-conductorsis given by equation (6)$M_{1} = {\left( \frac{\mu_{0} \cdot L_{1}}{\pi} \right) \cdot \left\{ {{\left( {1 + \frac{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{o}}{4 \cdot L_{1}} \right)}{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}} \right) \cdot {\ln\left( {1 + \frac{\sqrt{1 - \left( \frac{W_{1}}{2 \cdot L_{1}} \right)^{2}}}{\left( \frac{2 \cdot L_{1}}{W_{1}} \right) \cdot \left( \frac{d_{o}}{4 \cdot L_{1}} \right)}} \right)}} - 1} \right\}}$in said first section and by equation (7)$M_{2} = {\left( \frac{{- \mu_{0}} \cdot L_{2}}{\pi} \right) \cdot {{\ln\left( {1 + \frac{2 \cdot W_{2}}{d_{o}}} \right)}.}}$in said second section.
 26. The low-inductance cable of claim 24 whereinmutual inductance coupling between coaxial cable shields andcenter-conductors is given by equations (7)$M_{2} = {\left( \frac{{- \mu_{0}} \cdot L_{2}}{\pi} \right) \cdot {{\ln\left( {1 + \frac{2 \cdot W_{2}}{d_{o}}} \right)}.}}$in said third section.